The present invention relates generally to nuclear magnetic resonance and, more particularly, to a method and a system for measuring the diffusion tensor and for generating images related thereto.
Conventional nuclear magnetic resonance (NMR) has long been used for structural studies and compound identification based on the sensitivity of NMR parameters to the local chemical environment and to molecular mobilities. Further, conventional magnetic resonance imaging (MRI) is also well established as a technique for elucidating structure where it is used, for example, to discriminate between normal and pathological tissue. Such contrast depends on differences in parameters such as the proton density, the longitudinal relaxation time T.sub.1, and the transverse relaxation time T.sub.2 for different media. MRI has further been extended to imaging in which parameters such as the magnitude and phase of the tranverse magnetization, the magnitude of the longitudinal magnetization, and the resonance frequency are related to functions such as molecular displacements (e.g., flow and diffusion). One application, spectroscopic imaging techniques, provide a means for studying the spatial concentration of metabolites.
In another technique, diffusion NMR spectroscopy, a scalar diffusivity parameter is measured. The scalar diffusivity, D, which appears in Fick's first law, relating the concentration gradient of a spin-labeled species, .gradient.C, and its flux, J (i.e., J=-D.gradient.C) in water and other isotropic media, has been measured accurately using NMR spin-echo (H. Y. Carr, and E. M. Purcell, Phys. Rev., 94, 630, (1954); E. L. Hahn, Phys. Rev., 80, 580, (1950).) and pulsed-gradient spin-echo (E. O. Stejskal, and J. E. Tanner, J. Chem. Phys., 42, 288, (1965)) sequences. This modality exploits the random nature of molecular motion of the spin labeled species in diffusion which induces a phase dispersion resulting in the attenuation of the signal amplitude. The scalar self-diffusivity can be estimated from the linear relationship between the logarithm of the echo intensity and the square of the magnitude of the magnetic field gradient in which D appears as a constant of proportionality (See supra, Carr and Purcell; E. O. Stejskal, and J. E. Tanner, J. Chem. Phys., 42, 288, (1965). Recently, diffusion NMR spectroscopy and Fourier NMR imaging were combined (D. G. Taylor, and M. C. Bushell, Phys. Med. Biol., 30, 345, (1985); K. D. Merboldt et al., J. Magn. Reson., 64, 479, (1985); D. LeBihan, and E. Breton, Cr. Acad. Sci. (Paris), 301, 1109, (1985)) by combining a diffusion spectroscopy sequence with an imaging sequence, permitting an effective scalar diffusivity, D.sup.eff, to be estimated in each voxel of an image (D. LeBihan, Magn. Res. Quart., 7, 1, (1991)).
In contrast to isotropic media, one observes significantly different effective diffusion constants in anisotropic media when magnetic field gradients are applied in different directions. For instance, in diffusion NMR spectroscopy and imaging of anisotropic tissue like brain white matter (M. E. Moseley et al., Radiology, 176, 439, (1990)) or skeletal muscle (G. G. Cleveland et at., Biophys. J., 16, 1043, (1976)), the observed echo intensity depends on the specimen's orientation with respect to the direction of the applied magnetic field gradient. This orientation dependence of diffusion can be described by a generalized Fick's law (i.e., J=-D.sup.eff .gradient.C) in which D.sup.eff is an effective diffusion tensor.
While its use has been suggested in NMR spectroscopy (See supra, Stejskal, and J. E. Tanner, (1965)) and imaging (See supra, LeBihan; R. Turner et al., Radiology, 177, 407, (1990)), an explicit relationship between the effective diffusion tensor and the NMR signal has not been elucidated. Moreover, no method has been proposed to measure the off-diagonal elements of D.sup.eff. Although differences among D.sup.eff's diagonal elements are a necessary condition to demonstrate anisotropic diffusion, all diagonal and off-diagonal elements of D.sup.eff must be known to characterize diffusion adequately, specifically; to infer the mean microscopic displacements of the labelled species.
Thus, it would be advantageous to develop additional NMR measurement and imaging modalities based on the effective diffusion tensor.
Accordingly, an object of the present invention is to provide a new NMR modality to measure the effective diffusion tensor for spin-labelled species.
A related object of the present invention is to relate the effective diffusion tensor to physical characteristics of the observed sample.
Yet a further object of the present invention is to provide new MRI imaging modalities that use information contained in the diffusion tensor.
The foregoing specific objects and advantages of the invention are illustrative of those which can be achieved by the present invention and are not intended to be exhaustive or limiting of the possible advantages which can be realized. Thus, these and other objects and advantages of the invention will be apparent from the description herein or can be learned from practicing the invention, both as embodied herein or as modified in view of any variations which may be apparent to those skilled in the art.